# Lesson Worksheet: Triangles and Coordinate Proofs Mathematics

In this worksheet, we will practice finding the vertices and side lengths of a triangle on the coordinate plane and using them to write a coordinate proof.

Q1:

Give the coordinates of the vertices , , and . • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q2:

Give the coordinates of the vertices and . • A
• B
• C
• D
• E

Q3:

An isosceles triangle has vertices , , and . Find the length of the line segment drawn from to which is perpendicular to .

• A length units
• B length units
• C length units
• D length units

Q4:

A triangle is drawn in the coordinate plane with its vertices at , , and .

Find the length of the base .

Find the height of the triangle.

Hence, find the area of the triangle.

• A12.5 square units
• B25 square units
• C6.25 square units
• D10 square units
• E22.5 square units

Q5:

Given that is an isosceles triangle, where the coordinates of the points , , and are , , and , find the area of .

Q6:

A triangle has vertices at the points , , and with coordinates , , and respectively.

Work out the perimeter of the triangle . Give your solution to two decimal places.

Work out the area of the triangle .

Q7:

A triangle has vertices at the points , , and with coordinates , , and respectively.

Work out the perimeter of the triangle . Give your solution to one decimal place.

By drawing a rectangle through the vertices of the triangle, or otherwise, work out the area of the triangle .

Q8:

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the area of the triangle .

Q9:

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the perimeter of the triangle . Give your solution to two decimal places.

Q10:

Find the length of the base of Triangle B. 